US7555331B2 - Method for surgical navigation utilizing scale-invariant registration between a navigation system and a localization system - Google Patents
Method for surgical navigation utilizing scale-invariant registration between a navigation system and a localization system Download PDFInfo
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- US7555331B2 US7555331B2 US10/926,782 US92678204A US7555331B2 US 7555331 B2 US7555331 B2 US 7555331B2 US 92678204 A US92678204 A US 92678204A US 7555331 B2 US7555331 B2 US 7555331B2
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/70—Determining position or orientation of objects or cameras
- G06T7/73—Determining position or orientation of objects or cameras using feature-based methods
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/30—Determination of transform parameters for the alignment of images, i.e. image registration
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Abstract
Description
{right arrow over (X)} 1=({right arrow over (X)} B −{right arrow over (X)} A); {right arrow over (X)}′ 1({right arrow over (X)}′ B −{right arrow over (X)}′ A)
{right arrow over (X)} 2=({right arrow over (X)} C −{right arrow over (X)} B); {right arrow over (X)}′ 2=({right arrow over (X)}′ C −{right arrow over (X)}′ B)
{right arrow over (X)} 3=({right arrow over (X)} D −{right arrow over (X)} C); {right arrow over (X)}′ 3=({right arrow over (X)}′ D −{right arrow over (X)}′ C)
{right arrow over (X)} 4=({right arrow over (X)} A −{right arrow over (X)} D); {right arrow over (X)} 4′=({right arrow over (X)}′ A −{right arrow over (X)}′ D) (1)
{right arrow over (u)}′=PR{right arrow over (u)} (2)
where {right arrow over (u)}′ is a projection in the local frame of vector {right arrow over (u)} in the global frame. Thus, {right arrow over (X)}′1 (“primed” quantities are defined in the localization display, while “unprimed” quantities are the corresponding quantities defined in the navigation system) would be the projection of the rotated vector R{right arrow over (x)}. This projected vector generally has local frame components (v, w, 0), and can be written as:
From the above, three independent ratios of the lengths constructed from the vectors defined in equation (1) can be used to determine the three degrees of freedom associated with the rotation matrix R, and can be defined as:
l 1 ={right arrow over (X)}′ 1 T {right arrow over (X)}′ 1 ={right arrow over (X)} 1 T R T P R {right arrow over (X)} 1
l 2 ={right arrow over (X)}′ 2 T {right arrow over (X)}′ 2 ={right arrow over (X)} 2 T R T P R {right arrow over (X)} 2
l 3 ={right arrow over (X)}′ 3 T {right arrow over (X′)} 3 ={right arrow over (X)} 3 T R T P R {right arrow over (X)} 3
l 4 ={right arrow over (X)}′ 4 T {right arrow over (X)}′ 4 ={right arrow over (X)} 4 T R T P R {right arrow over (X)} 4 (4)
From the above, three independent ratios of the lengths constructed from the vectors defined in equation (4) can be used to determine the three degrees of freedom associated with the rotation matrix R. From these ratios of distances, a cost function can be constructed for defining an error associated with a given rotation matrix, as defined below:
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US10/926,782 US7555331B2 (en) | 2004-08-26 | 2004-08-26 | Method for surgical navigation utilizing scale-invariant registration between a navigation system and a localization system |
PCT/US2005/030477 WO2006026465A2 (en) | 2004-08-26 | 2005-08-26 | Surgical navigation and localization system utlizing scale-invariant registration |
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US10/926,782 US7555331B2 (en) | 2004-08-26 | 2004-08-26 | Method for surgical navigation utilizing scale-invariant registration between a navigation system and a localization system |
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US20060058646A1 (en) | 2006-03-16 |
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